{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RVU1Q900Dl2r"
      },
      "source": [
        "##### Copyright 2020 The TensorFlow Authors.\n",
        "##### Copyright 2020 Sen Pei (Columbia University).\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "id": "QKUGkj9ZDmfg"
      },
      "outputs": [],
      "source": [
        "#@title Licensed under the Apache License, Version 2.0 (the \"License\"); { display-mode: \"form\" }\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "# https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KCZNiAlqEAr1"
      },
      "source": [
        "# Substantial Undocumented Infection Facilitates the Rapid Dissemination of Novel Coronavirus (SARS-CoV2)\n",
        "\n",
        "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://www.tensorflow.org/probability/examples/Undocumented_Infection_and_the_Dissemination_of_SARS-CoV2\"><img src=\"https://www.tensorflow.org/images/tf_logo_32px.png\" />View on TensorFlow.org</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Undocumented_Infection_and_the_Dissemination_of_SARS-CoV2.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Undocumented_Infection_and_the_Dissemination_of_SARS-CoV2.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View source on GitHub</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a href=\"https://storage.googleapis.com/tensorflow_docs/probability/tensorflow_probability/examples/jupyter_notebooks/Undocumented_Infection_and_the_Dissemination_of_SARS-CoV2.ipynb\"><img src=\"https://www.tensorflow.org/images/download_logo_32px.png\" />Download notebook</a>\n",
        "  </td>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iBdidAV1Rw-G"
      },
      "source": [
        "This is a TensorFlow Probability port of the eponymous 16 March 2020 paper by Li et al.  We faithfully reproduce the original authors' methods and results on the TensorFlow Probability platform, showcasing some of TFP's capabilities in the setting of modern epidemiology modeling.  Porting to TensorFlow gives us a ~10x speedup relative to the original Matlab code, and, since TensorFlow Probability pervasively supports vectorized batch computation, also favorably scales to hundreds of independent replications.\n",
        "\n",
        "### Original paper\n",
        "\n",
        "Ruiyun Li, Sen Pei, Bin Chen, Yimeng Song, Tao Zhang, Wan Yang, and Jeffrey Shaman. Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV2). (2020), doi:\n",
        "https://doi.org/10.1126/science.abb3221 .\n",
        "\n",
        "*Abstract:* \"Estimation of the prevalence and contagiousness of undocumented novel coronavirus (SARS-CoV2) infections is critical for understanding the overall prevalence and pandemic potential of this disease. Here we use observations of reported infection within China, in conjunction with mobility data, a networked dynamic metapopulation model and Bayesian inference, to infer critical epidemiological characteristics associated with SARS-CoV2, including the fraction of undocumented infections and their contagiousness. We estimate 86% of all infections were undocumented (95% CI: [82%–90%]) prior to 23 January 2020 travel restrictions. Per person, the transmission rate of undocumented infections was 55% of documented infections ([46%–62%]), yet, due to their greater numbers, undocumented infections were the infection source for 79% of documented cases. These findings explain the rapid geographic spread of SARS-CoV2 and indicate containment of this virus will be particularly challenging.\"\n",
        "\n",
        "[Github link](https://github.com/SenPei-CU/COVID-19) to the code and data."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0yETSzjhoVBN"
      },
      "source": [
        "## Overview"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HtZGdFItx4Z3"
      },
      "source": [
        "The model is a [compartmental disease model](https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology), with compartments for \"susceptible\", \"exposed\" (infected but not yet infectious), \"never-documented infectious\", and \"eventually-documented infectious\". There are two noteworthy features: separate compartments for each of 375 Chinese cities, with an assumption about how people travel from one city to another; and delays in reporting infection, so that a case that becomes \"eventually-documented infectious\" on day $t$ doesn't show up in the observed case counts until a stochastic later day.\n",
        "\n",
        "The model assumes that the never-documented cases end up undocumented by being milder, and thus infect others at a lower rate.  The main parameter of interest in the original paper is the proportion of cases that go undocumented, to estimate both the extent of existing infection, and the impact of undocumented transmission on the spread of the disease.\n",
        "\n",
        "This colab is structured as a code walkthrough in bottom-up style.  In order, we will\n",
        "- Ingest and briefly examine the data,\n",
        "- Define the state space and dynamics of the model,\n",
        "- Build up a suite of functions for doing inference in the model following Li et al, and\n",
        "- Invoke them and examine the results.  Spoiler: They come out the same as the paper.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Brvp_GH-ItsG"
      },
      "source": [
        "## Installation and Python Imports"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "iUEZ07T3yuBj"
      },
      "outputs": [],
      "source": [
        "!pip3 install -q tf-nightly tfp-nightly"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-Za3hnj2y5M9"
      },
      "outputs": [],
      "source": [
        "from __future__ import absolute_import\n",
        "from __future__ import division\n",
        "from __future__ import print_function\n",
        "\n",
        "import collections\n",
        "import io\n",
        "import requests\n",
        "import time\n",
        "import zipfile\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "\n",
        "import tensorflow.compat.v2 as tf\n",
        "import tensorflow_probability as tfp\n",
        "from tensorflow_probability.python.internal import samplers\n",
        "\n",
        "tfd = tfp.distributions\n",
        "tfes = tfp.experimental.sequential"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KYfPl6uqzIs1"
      },
      "source": [
        "## Data Import\n",
        "\n",
        "Let's import the data from github and inspect some of it."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1q22N4rPzXIg"
      },
      "outputs": [],
      "source": [
        "r = requests.get('https://raw.githubusercontent.com/SenPei-CU/COVID-19/master/Data.zip')\n",
        "z = zipfile.ZipFile(io.BytesIO(r.content))\n",
        "z.extractall('/tmp/')\n",
        "raw_incidence = pd.read_csv('/tmp/data/Incidence.csv')\n",
        "raw_mobility = pd.read_csv('/tmp/data/Mobility.csv')\n",
        "raw_population = pd.read_csv('/tmp/data/pop.csv')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IC3Nt8lJSllh"
      },
      "source": [
        "Below we can see the raw incidence count per day. We are most interested in the first 14 days (January 10th to January 23rd), as the travel restrictions were put in place on the 23rd.  The paper deals with this by modeling Jan 10-23 and Jan 23+ separately, with different parameters; we will just restrict our reproduction to the earlier period."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yFP-Tah4zfne"
      },
      "outputs": [
        {
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>5</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>8</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>7</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>12</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>5</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>7</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>13</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>5</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>6</td>\n",
              "      <td>1</td>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>...</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>15</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>7</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>15</td>\n",
              "      <td>7</td>\n",
              "      <td>8</td>\n",
              "      <td>4</td>\n",
              "      <td>...</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>17</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>13</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>14</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>12</td>\n",
              "      <td>8</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>13</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>5</td>\n",
              "      <td>2</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>5</td>\n",
              "      <td>4</td>\n",
              "      <td>28</td>\n",
              "      <td>3</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>11</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>7</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>14</td>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>8</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>5</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>19</td>\n",
              "      <td>3</td>\n",
              "      <td>54</td>\n",
              "      <td>3</td>\n",
              "      <td>...</td>\n",
              "      <td>8</td>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>5</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>20</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>5</td>\n",
              "      <td>1</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>21</td>\n",
              "      <td>5</td>\n",
              "      <td>1</td>\n",
              "      <td>7</td>\n",
              "      <td>2</td>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>18</td>\n",
              "      <td>21</td>\n",
              "      <td>58</td>\n",
              "      <td>2</td>\n",
              "      <td>...</td>\n",
              "      <td>6</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>21</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>6</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>27</td>\n",
              "      <td>6</td>\n",
              "      <td>2</td>\n",
              "      <td>5</td>\n",
              "      <td>3</td>\n",
              "      <td>8</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>16</td>\n",
              "      <td>5</td>\n",
              "      <td>55</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>14</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>4</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>24</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>7</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>25</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>5</td>\n",
              "      <td>1</td>\n",
              "      <td>13</td>\n",
              "      <td>9</td>\n",
              "      <td>14</td>\n",
              "      <td>2</td>\n",
              "      <td>...</td>\n",
              "      <td>6</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>23</td>\n",
              "      <td>12</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>9</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>24</td>\n",
              "      <td>7</td>\n",
              "      <td>6</td>\n",
              "      <td>7</td>\n",
              "      <td>1</td>\n",
              "      <td>4</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>12</td>\n",
              "      <td>11</td>\n",
              "      <td>24</td>\n",
              "      <td>1</td>\n",
              "      <td>...</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>8</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>39</td>\n",
              "      <td>7</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>12</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>16</td>\n",
              "      <td>5</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>6</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>8</td>\n",
              "      <td>9</td>\n",
              "      <td>26</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>8</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>16</td>\n",
              "      <td>12</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>18</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>6</td>\n",
              "      <td>0</td>\n",
              "      <td>15</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>8</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>14</td>\n",
              "      <td>27</td>\n",
              "      <td>49</td>\n",
              "      <td>4</td>\n",
              "      <td>...</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>8</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25</th>\n",
              "      <td>25</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>10</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>10</td>\n",
              "      <td>14</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>14</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>6</td>\n",
              "      <td>5</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>9</td>\n",
              "      <td>18</td>\n",
              "      <td>24</td>\n",
              "      <td>4</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>26</th>\n",
              "      <td>21</td>\n",
              "      <td>11</td>\n",
              "      <td>3</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>9</td>\n",
              "      <td>6</td>\n",
              "      <td>9</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>21</td>\n",
              "      <td>5</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>5</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>8</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>10</td>\n",
              "      <td>6</td>\n",
              "      <td>31</td>\n",
              "      <td>3</td>\n",
              "      <td>...</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>10</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27</th>\n",
              "      <td>23</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>12</td>\n",
              "      <td>1</td>\n",
              "      <td>8</td>\n",
              "      <td>0</td>\n",
              "      <td>16</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>10</td>\n",
              "      <td>0</td>\n",
              "      <td>16</td>\n",
              "      <td>5</td>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>9</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>5</td>\n",
              "      <td>10</td>\n",
              "      <td>25</td>\n",
              "      <td>5</td>\n",
              "      <td>...</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>28</th>\n",
              "      <td>18</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>6</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>12</td>\n",
              "      <td>8</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>6</td>\n",
              "      <td>5</td>\n",
              "      <td>17</td>\n",
              "      <td>2</td>\n",
              "      <td>...</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>8</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>29</th>\n",
              "      <td>11</td>\n",
              "      <td>7</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>14</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>6</td>\n",
              "      <td>6</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>5</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>5</td>\n",
              "      <td>10</td>\n",
              "      <td>1</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>8</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>30 rows × 375 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "    Beijing  Tianjin  Shijiazhuang  Tangshan  Qinhuangdao  Handan  Xintai  Baoding  ...  Kekedala  Taiwan  Hongkong  Macao  Hetianxian (Xinjiang)  Moyu  Yutian  Gejiu\n",
              "0         0        0             0         0            0       0       0        0  ...         0       0         0      0                      0     0       0      0\n",
              "1         0        0             0         0            0       0       0        0  ...         0       0         0      0                      0     0       0      0\n",
              "2         0        0             0         0            0       0       0        0  ...         0       0         0      0                      0     0       0      0\n",
              "3         0        0             0         0            0       0       0        0  ...         0       0         0      0                      0     0       0      0\n",
              "4         0        0             0         0            0       0       0        0  ...         0       0         0      0                      0     0       0      0\n",
              "5         0        0             0         0            0       0       0        0  ...         0       0         0      0                      0     0       0      0\n",
              "6         0        0             0         0            0       0       0        0  ...         0       0         0      0                      0     0       0      0\n",
              "7         0        0             0         0            0       0       0        0  ...         0       0         0      0                      0     0       0      0\n",
              "8         0        0             0         0            0       0       0        0  ...         0       0         0      0                      0     0       0      0\n",
              "9         0        0             0         0            0       0       0        0  ...         0       0         0      0                      0     0       0      0\n",
              "10        5        0             0         0            0       0       0        0  ...         0       0         0      0                      0     0       0      0\n",
              "11        5        2             0         0            0       0       0        0  ...         0       1         0      0                      0     0       0      0\n",
              "12        4        2             1         0            0       0       0        0  ...         0       0         0      0                      0     0       0      0\n",
              "13       12        1             0         0            0       0       0        0  ...         0       0         0      0                      0     0       0      0\n",
              "14        7        2             3         0            0       0       0        1  ...         0       0         0      0                      0     0       0      0\n",
              "15       15        2             1         0            0       2       0        2  ...         0       0         3      0                      0     0       0      0\n",
              "16       17        4             2         0            0       0       1        0  ...         0       0         0      0                      0     0       0      0\n",
              "17       12        8             2         1            0       2       1        0  ...         0       1         0      0                      0     0       0      0\n",
              "18       11        1             1         2            0       0       1        3  ...         0       1         0      0                      0     0       0      0\n",
              "19       20        3             1         0            0       2       2        1  ...         0       0         0      0                      0     0       0      0\n",
              "20       21        3             0         4            0       1       2        4  ...         0       0         0      0                      0     0       0      0\n",
              "21       24        0             1         1            1       3       3        0  ...         0       0         0      0                      0     0       0      0\n",
              "22       23       12             1         3            0       1       0        2  ...         0       0         0      0                      0     0       0      0\n",
              "23       39        7             3         0            1       0       4        0  ...         0       0         0      0                      0     0       0      0\n",
              "24       16       12             5         0            0       3       2        0  ...         0       0         0      0                      0     0       0      0\n",
              "25       25        0             0         1            1       0       0        4  ...         0       0         0      0                      0     0       0      0\n",
              "26       21       11             3         5            0       4       3        0  ...         0       0         0      0                      0     0       0      0\n",
              "27       23        0             0         2            2       4       0        1  ...         0       0         0      0                      0     0       0      0\n",
              "28       18        0             0         4            2       4       2        0  ...         0       0         0      0                      0     0       0      0\n",
              "29       11        7             0         4            0       1       0        3  ...         0       0         0      0                      0     0       0      0\n",
              "\n",
              "[30 rows x 375 columns]"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "raw_incidence.drop('Date', axis=1)  # The 'Date' column is all 1/18/21\n",
        "# Luckily the days are in order, starting on January 10th, 2020."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EOQn3GZ2DcKE"
      },
      "source": [
        "Let's sanity-check the Wuhan incidence counts."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "S6iXSZK7Df5h"
      },
      "outputs": [
        {
          "data": {
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Qu9TSboD6WqtZ7QGd+HweliSOQW6JBpd6WQ2ssKIeOgPrV8+gTpEWXmCGkgAh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\n/4Qe9HSAXAWqAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 600x400 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(raw_incidence.Wuhan, '.-')\n",
        "plt.title('Wuhan incidence counts over 1/10/20 - 02/08/20')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4rzCbKNkMKdk"
      },
      "source": [
        "So far, so good.  Now the initial population counts."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "P2Spczra1A7y"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>City</th>\n",
              "      <th>Population</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Beijing</td>\n",
              "      <td>21540000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Tianjin</td>\n",
              "      <td>11760000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Shijiazhuang</td>\n",
              "      <td>10151200.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Tangshan</td>\n",
              "      <td>7843600.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Qinhuangdao</td>\n",
              "      <td>3094600.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>Handan</td>\n",
              "      <td>9492800.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>Xintai</td>\n",
              "      <td>7319900.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>Baoding</td>\n",
              "      <td>10425300.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>Zhangjiakou</td>\n",
              "      <td>4425100.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>Chengde</td>\n",
              "      <td>3531800.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>Cangzhou</td>\n",
              "      <td>7505500.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>Langfang</td>\n",
              "      <td>4615000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>Hengshui</td>\n",
              "      <td>4453100.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>Taiyuan</td>\n",
              "      <td>4421400.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>Datong</td>\n",
              "      <td>3456000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>Yangquan</td>\n",
              "      <td>1414400.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>Changzhi</td>\n",
              "      <td>3468200.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>Jincheng</td>\n",
              "      <td>2343100.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>Shuozhou</td>\n",
              "      <td>1781200.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>Jinzhong</td>\n",
              "      <td>3381600.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>Yuncheng</td>\n",
              "      <td>5359600.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>Xinzhou</td>\n",
              "      <td>3171200.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>Linfen</td>\n",
              "      <td>4500300.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>Lvliang</td>\n",
              "      <td>3885600.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>Huhehaote</td>\n",
              "      <td>2437900.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25</th>\n",
              "      <td>Baotou</td>\n",
              "      <td>2297400.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>26</th>\n",
              "      <td>Wuhai</td>\n",
              "      <td>434900.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27</th>\n",
              "      <td>Chifeng</td>\n",
              "      <td>4518000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>28</th>\n",
              "      <td>Tongliao</td>\n",
              "      <td>3083500.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>29</th>\n",
              "      <td>Eerduosi</td>\n",
              "      <td>2078400.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>345</th>\n",
              "      <td>Urumuqi</td>\n",
              "      <td>2330000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>346</th>\n",
              "      <td>Kelamayi</td>\n",
              "      <td>270000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>347</th>\n",
              "      <td>Tulufan</td>\n",
              "      <td>590000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>348</th>\n",
              "      <td>Hami</td>\n",
              "      <td>550000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>349</th>\n",
              "      <td>Changji</td>\n",
              "      <td>1590000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>350</th>\n",
              "      <td>Bozhou (Xinjiang)</td>\n",
              "      <td>470000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>351</th>\n",
              "      <td>Bazhou (Xinjiang)</td>\n",
              "      <td>1170000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>352</th>\n",
              "      <td>Akesu</td>\n",
              "      <td>2260000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>353</th>\n",
              "      <td>Kezhou</td>\n",
              "      <td>470000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>354</th>\n",
              "      <td>Kashi</td>\n",
              "      <td>3650000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>355</th>\n",
              "      <td>Hetian (Xinjiang)</td>\n",
              "      <td>1800000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>356</th>\n",
              "      <td>Yili</td>\n",
              "      <td>2600000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>357</th>\n",
              "      <td>Tacheng</td>\n",
              "      <td>990000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>358</th>\n",
              "      <td>Aletai</td>\n",
              "      <td>640000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>359</th>\n",
              "      <td>Shihezi</td>\n",
              "      <td>660000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>360</th>\n",
              "      <td>Ala'er</td>\n",
              "      <td>326800.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>361</th>\n",
              "      <td>Tumushuke</td>\n",
              "      <td>255600.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>362</th>\n",
              "      <td>Wujiaqu (Xinjiang)</td>\n",
              "      <td>125600.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>363</th>\n",
              "      <td>Beitun</td>\n",
              "      <td>80000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>364</th>\n",
              "      <td>Wujiaqushi (Xinjiang)</td>\n",
              "      <td>125600.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>365</th>\n",
              "      <td>Tiemenguan</td>\n",
              "      <td>50000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>366</th>\n",
              "      <td>Shuanghe</td>\n",
              "      <td>53800.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>367</th>\n",
              "      <td>Kekedala</td>\n",
              "      <td>75000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>368</th>\n",
              "      <td>Taiwan</td>\n",
              "      <td>23580000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>369</th>\n",
              "      <td>Hongkong</td>\n",
              "      <td>7450000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>370</th>\n",
              "      <td>Macao</td>\n",
              "      <td>630000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>371</th>\n",
              "      <td>Hetianxian (Xinjiang)</td>\n",
              "      <td>360000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>372</th>\n",
              "      <td>Moyu</td>\n",
              "      <td>646200.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>373</th>\n",
              "      <td>Yutian</td>\n",
              "      <td>289500.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>374</th>\n",
              "      <td>Gejiu</td>\n",
              "      <td>472000.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>375 rows × 2 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "                      City  Population\n",
              "0                  Beijing  21540000.0\n",
              "1                  Tianjin  11760000.0\n",
              "2             Shijiazhuang  10151200.0\n",
              "3                 Tangshan   7843600.0\n",
              "4              Qinhuangdao   3094600.0\n",
              "5                   Handan   9492800.0\n",
              "6                   Xintai   7319900.0\n",
              "7                  Baoding  10425300.0\n",
              "8              Zhangjiakou   4425100.0\n",
              "9                  Chengde   3531800.0\n",
              "10                Cangzhou   7505500.0\n",
              "11                Langfang   4615000.0\n",
              "12                Hengshui   4453100.0\n",
              "13                 Taiyuan   4421400.0\n",
              "14                  Datong   3456000.0\n",
              "15                Yangquan   1414400.0\n",
              "16                Changzhi   3468200.0\n",
              "17                Jincheng   2343100.0\n",
              "18                Shuozhou   1781200.0\n",
              "19                Jinzhong   3381600.0\n",
              "20                Yuncheng   5359600.0\n",
              "21                 Xinzhou   3171200.0\n",
              "22                  Linfen   4500300.0\n",
              "23                 Lvliang   3885600.0\n",
              "24               Huhehaote   2437900.0\n",
              "25                  Baotou   2297400.0\n",
              "26                   Wuhai    434900.0\n",
              "27                 Chifeng   4518000.0\n",
              "28                Tongliao   3083500.0\n",
              "29                Eerduosi   2078400.0\n",
              "..                     ...         ...\n",
              "345                Urumuqi   2330000.0\n",
              "346               Kelamayi    270000.0\n",
              "347                Tulufan    590000.0\n",
              "348                   Hami    550000.0\n",
              "349                Changji   1590000.0\n",
              "350      Bozhou (Xinjiang)    470000.0\n",
              "351      Bazhou (Xinjiang)   1170000.0\n",
              "352                  Akesu   2260000.0\n",
              "353                 Kezhou    470000.0\n",
              "354                  Kashi   3650000.0\n",
              "355      Hetian (Xinjiang)   1800000.0\n",
              "356                   Yili   2600000.0\n",
              "357                Tacheng    990000.0\n",
              "358                 Aletai    640000.0\n",
              "359                Shihezi    660000.0\n",
              "360                 Ala'er    326800.0\n",
              "361              Tumushuke    255600.0\n",
              "362     Wujiaqu (Xinjiang)    125600.0\n",
              "363                 Beitun     80000.0\n",
              "364  Wujiaqushi (Xinjiang)    125600.0\n",
              "365             Tiemenguan     50000.0\n",
              "366               Shuanghe     53800.0\n",
              "367               Kekedala     75000.0\n",
              "368                 Taiwan  23580000.0\n",
              "369               Hongkong   7450000.0\n",
              "370                  Macao    630000.0\n",
              "371  Hetianxian (Xinjiang)    360000.0\n",
              "372                   Moyu    646200.0\n",
              "373                 Yutian    289500.0\n",
              "374                  Gejiu    472000.0\n",
              "\n",
              "[375 rows x 2 columns]"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "raw_population"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Xf6xLARfsBwe"
      },
      "source": [
        "Let's also check and record which entry is Wuhan."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "phQQFI401Pr8"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "'Wuhan'"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "raw_population['City'][169]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "uS5vWXkBsQLG"
      },
      "outputs": [],
      "source": [
        "WUHAN_IDX = 169"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3RWGcEfL65sS"
      },
      "source": [
        "And here we see the mobility matrix between different cities. This is a proxy for the number of people moving between different cities on the first 14 days.  It's dervied from GPS records provided by Tencent for the 2018 Lunar New Year season.  Li et al model mobility during the 2020 season as some unknown (subject to inference) constant factor $\\theta$ times this."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "BvPonRBJ1AIQ"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Day</th>\n",
              "      <th>Origin</th>\n",
              "      <th>Destination</th>\n",
              "      <th>Mobility Index</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>Beijing</td>\n",
              "      <td>Tianjin</td>\n",
              "      <td>17585</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>Beijing</td>\n",
              "      <td>Shijiazhuang</td>\n",
              "      <td>21289</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1</td>\n",
              "      <td>Beijing</td>\n",
              "      <td>Handan</td>\n",
              "      <td>27676</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1</td>\n",
              "      <td>Beijing</td>\n",
              "      <td>Baoding</td>\n",
              "      <td>19007</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1</td>\n",
              "      <td>Beijing</td>\n",
              "      <td>Zhangjiakou</td>\n",
              "      <td>20327</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>1</td>\n",
              "      <td>Beijing</td>\n",
              "      <td>Langfang</td>\n",
              "      <td>31180</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>1</td>\n",
              "      <td>Beijing</td>\n",
              "      <td>Ha'erbin</td>\n",
              "      <td>24390</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>1</td>\n",
              "      <td>Beijing</td>\n",
              "      <td>Shanghai</td>\n",
              "      <td>66799</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>1</td>\n",
              "      <td>Beijing</td>\n",
              "      <td>Nanjing</td>\n",
              "      <td>17719</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>1</td>\n",
              "      <td>Beijing</td>\n",
              "      <td>Hangzhou</td>\n",
              "      <td>28536</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>1</td>\n",
              "      <td>Beijing</td>\n",
              "      <td>Wenzhou</td>\n",
              "      <td>16767</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>1</td>\n",
              "      <td>Beijing</td>\n",
              "      <td>Xinyang</td>\n",
              "      <td>17522</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>1</td>\n",
              "      <td>Beijing</td>\n",
              "      <td>Wuhan</td>\n",
              "      <td>32517</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>1</td>\n",
              "      <td>Beijing</td>\n",
              "      <td>Changsha</td>\n",
              "      <td>35671</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>1</td>\n",
              "      <td>Beijing</td>\n",
              "      <td>Chongqing</td>\n",
              "      <td>66639</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>1</td>\n",
              "      <td>Beijing</td>\n",
              "      <td>Xi'an</td>\n",
              "      <td>17088</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>1</td>\n",
              "      <td>Tianjin</td>\n",
              "      <td>Beijing</td>\n",
              "      <td>13942</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>1</td>\n",
              "      <td>Tianjin</td>\n",
              "      <td>Tangshan</td>\n",
              "      <td>6631</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>1</td>\n",
              "      <td>Tianjin</td>\n",
              "      <td>Handan</td>\n",
              "      <td>5140</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>1</td>\n",
              "      <td>Tianjin</td>\n",
              "      <td>Baoding</td>\n",
              "      <td>6398</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>1</td>\n",
              "      <td>Tianjin</td>\n",
              "      <td>Cangzhou</td>\n",
              "      <td>7030</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>1</td>\n",
              "      <td>Tianjin</td>\n",
              "      <td>Langfang</td>\n",
              "      <td>7363</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>1</td>\n",
              "      <td>Tianjin</td>\n",
              "      <td>Changchun</td>\n",
              "      <td>4258</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>1</td>\n",
              "      <td>Tianjin</td>\n",
              "      <td>Ha'erbin</td>\n",
              "      <td>12675</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>1</td>\n",
              "      <td>Tianjin</td>\n",
              "      <td>Shanghai</td>\n",
              "      <td>8698</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25</th>\n",
              "      <td>1</td>\n",
              "      <td>Tianjin</td>\n",
              "      <td>Hangzhou</td>\n",
              "      <td>4364</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>26</th>\n",
              "      <td>1</td>\n",
              "      <td>Tianjin</td>\n",
              "      <td>Fuzhou (Fujian)</td>\n",
              "      <td>14632</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27</th>\n",
              "      <td>1</td>\n",
              "      <td>Tianjin</td>\n",
              "      <td>Dezhou</td>\n",
              "      <td>6857</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>28</th>\n",
              "      <td>1</td>\n",
              "      <td>Tianjin</td>\n",
              "      <td>Wuhan</td>\n",
              "      <td>4669</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>29</th>\n",
              "      <td>1</td>\n",
              "      <td>Tianjin</td>\n",
              "      <td>Changsha</td>\n",
              "      <td>6579</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92218</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Changsha</td>\n",
              "      <td>52</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92219</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Hengyang</td>\n",
              "      <td>42</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92220</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Changde</td>\n",
              "      <td>53</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92221</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Chenzhou</td>\n",
              "      <td>36</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92222</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Yongzhou</td>\n",
              "      <td>42</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92223</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Guangzhou</td>\n",
              "      <td>48</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92224</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Shenzhen</td>\n",
              "      <td>77</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92225</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Huizhou</td>\n",
              "      <td>43</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92226</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Nannig</td>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92227</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Beihai</td>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92228</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Baise</td>\n",
              "      <td>37</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92229</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Chongqing</td>\n",
              "      <td>132</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92230</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Neijiang</td>\n",
              "      <td>47</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92231</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Liupanshui</td>\n",
              "      <td>41</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92232</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Bijie</td>\n",
              "      <td>32</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92233</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Kunming</td>\n",
              "      <td>452</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92234</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Qujing</td>\n",
              "      <td>359</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92235</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Yuxi</td>\n",
              "      <td>170</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92236</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Shaotong</td>\n",
              "      <td>94</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92237</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Pu'er</td>\n",
              "      <td>50</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92238</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Chuxiong</td>\n",
              "      <td>62</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92239</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Wenshan</td>\n",
              "      <td>138</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92240</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Dali</td>\n",
              "      <td>50</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92241</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Xi'an</td>\n",
              "      <td>55</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92242</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Xianyang</td>\n",
              "      <td>38</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92243</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Lanzhou</td>\n",
              "      <td>60</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92244</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Pingliang</td>\n",
              "      <td>73</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92245</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Dongxi</td>\n",
              "      <td>126</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92246</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Xining</td>\n",
              "      <td>31</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92247</th>\n",
              "      <td>14</td>\n",
              "      <td>Gejiu</td>\n",
              "      <td>Guyuan</td>\n",
              "      <td>33</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>92248 rows × 4 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "       Day   Origin      Destination  Mobility Index\n",
              "0        1  Beijing          Tianjin           17585\n",
              "1        1  Beijing     Shijiazhuang           21289\n",
              "2        1  Beijing           Handan           27676\n",
              "3        1  Beijing          Baoding           19007\n",
              "4        1  Beijing      Zhangjiakou           20327\n",
              "5        1  Beijing         Langfang           31180\n",
              "6        1  Beijing         Ha'erbin           24390\n",
              "7        1  Beijing         Shanghai           66799\n",
              "8        1  Beijing          Nanjing           17719\n",
              "9        1  Beijing         Hangzhou           28536\n",
              "10       1  Beijing          Wenzhou           16767\n",
              "11       1  Beijing          Xinyang           17522\n",
              "12       1  Beijing            Wuhan           32517\n",
              "13       1  Beijing         Changsha           35671\n",
              "14       1  Beijing        Chongqing           66639\n",
              "15       1  Beijing            Xi'an           17088\n",
              "16       1  Tianjin          Beijing           13942\n",
              "17       1  Tianjin         Tangshan            6631\n",
              "18       1  Tianjin           Handan            5140\n",
              "19       1  Tianjin          Baoding            6398\n",
              "20       1  Tianjin         Cangzhou            7030\n",
              "21       1  Tianjin         Langfang            7363\n",
              "22       1  Tianjin        Changchun            4258\n",
              "23       1  Tianjin         Ha'erbin           12675\n",
              "24       1  Tianjin         Shanghai            8698\n",
              "25       1  Tianjin         Hangzhou            4364\n",
              "26       1  Tianjin  Fuzhou (Fujian)           14632\n",
              "27       1  Tianjin           Dezhou            6857\n",
              "28       1  Tianjin            Wuhan            4669\n",
              "29       1  Tianjin         Changsha            6579\n",
              "...    ...      ...              ...             ...\n",
              "92218   14    Gejiu         Changsha              52\n",
              "92219   14    Gejiu         Hengyang              42\n",
              "92220   14    Gejiu          Changde              53\n",
              "92221   14    Gejiu         Chenzhou              36\n",
              "92222   14    Gejiu         Yongzhou              42\n",
              "92223   14    Gejiu        Guangzhou              48\n",
              "92224   14    Gejiu         Shenzhen              77\n",
              "92225   14    Gejiu          Huizhou              43\n",
              "92226   14    Gejiu           Nannig              30\n",
              "92227   14    Gejiu           Beihai              30\n",
              "92228   14    Gejiu            Baise              37\n",
              "92229   14    Gejiu        Chongqing             132\n",
              "92230   14    Gejiu         Neijiang              47\n",
              "92231   14    Gejiu       Liupanshui              41\n",
              "92232   14    Gejiu            Bijie              32\n",
              "92233   14    Gejiu          Kunming             452\n",
              "92234   14    Gejiu           Qujing             359\n",
              "92235   14    Gejiu             Yuxi             170\n",
              "92236   14    Gejiu         Shaotong              94\n",
              "92237   14    Gejiu            Pu'er              50\n",
              "92238   14    Gejiu         Chuxiong              62\n",
              "92239   14    Gejiu          Wenshan             138\n",
              "92240   14    Gejiu             Dali              50\n",
              "92241   14    Gejiu            Xi'an              55\n",
              "92242   14    Gejiu         Xianyang              38\n",
              "92243   14    Gejiu          Lanzhou              60\n",
              "92244   14    Gejiu        Pingliang              73\n",
              "92245   14    Gejiu           Dongxi             126\n",
              "92246   14    Gejiu           Xining              31\n",
              "92247   14    Gejiu           Guyuan              33\n",
              "\n",
              "[92248 rows x 4 columns]"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "raw_mobility"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vSY98S14Oaqs"
      },
      "source": [
        "Finally, let's preprocess all this into numpy arrays that we can consume."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9txbadTC14YP"
      },
      "outputs": [],
      "source": [
        "# The given populations are only \"initial\" because of intercity mobility during\n",
        "# the holiday season.\n",
        "initial_population = raw_population['Population'].to_numpy().astype(np.float32)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w-pKDK461zFX"
      },
      "source": [
        "Convert the mobility data into an [L, L, T]-shaped Tensor, where L is the number of locations, and T is the number of timesteps."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "f-2zASNxw_wi"
      },
      "outputs": [],
      "source": [
        "daily_mobility_matrices = []\n",
        "for i in range(1, 15):\n",
        "  day_mobility = raw_mobility[raw_mobility['Day'] == i]\n",
        "  \n",
        "  # Make a matrix of daily mobilities.\n",
        "  z = pd.crosstab(\n",
        "      day_mobility.Origin, \n",
        "      day_mobility.Destination, \n",
        "      values=day_mobility['Mobility Index'], aggfunc='sum', dropna=False)\n",
        "  \n",
        "  # Include every city, even if there are no rows for some in the raw data on\n",
        "  # some day.  This uses the sort order of `raw_population`.\n",
        "  z = z.reindex(index=raw_population['City'], columns=raw_population['City'], \n",
        "                fill_value=0)\n",
        "  # Finally, fill any missing entries with 0. This means no mobility.\n",
        "  z = z.fillna(0)\n",
        "  daily_mobility_matrices.append(z.to_numpy())\n",
        "\n",
        "mobility_matrix_over_time = np.stack(daily_mobility_matrices, axis=-1).astype(\n",
        "    np.float32)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GaJYQFT91-15"
      },
      "source": [
        "Finally take the observed infections and make an [L, T] table."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "qs4TKTnv176D"
      },
      "outputs": [],
      "source": [
        "# Remove the date parameter and take the first 14 days.\n",
        "observed_daily_infectious_count = raw_incidence.to_numpy()[:14, 1:]\n",
        "observed_daily_infectious_count = np.transpose(\n",
        "    observed_daily_infectious_count).astype(np.float32)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B9WeGRug2HLQ"
      },
      "source": [
        "And double-check that we got the shapes the way we wanted.  As a reminder, we're working with 375 cities and 14 days."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "dymKgF8p1hgi"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Mobility Matrix over time should have shape (375, 375, 14): (375, 375, 14)\n",
            "Observed Infectious should have shape (375, 14): (375, 14)\n",
            "Initial population should have shape (375): (375,)\n"
          ]
        }
      ],
      "source": [
        "print('Mobility Matrix over time should have shape (375, 375, 14): {}'.format(\n",
        "    mobility_matrix_over_time.shape))\n",
        "print('Observed Infectious should have shape (375, 14): {}'.format(\n",
        "    observed_daily_infectious_count.shape))\n",
        "print('Initial population should have shape (375): {}'.format(\n",
        "    initial_population.shape))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LGTcVy2K2mxv"
      },
      "source": [
        "## Defining State and Parameters\n",
        "\n",
        "\n",
        "Let's start defining our model. The model we are reproducing is a variant of an [SEIR model](https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SEIR_model). In this case we have the following time-varying states:\n",
        "* $S$: Number of people susceptible to the disease in each city.\n",
        "* $E$: Number of people in each city exposed to the disease but not infectious yet.  Biologically, this corresponds to contracting the disease, in that all exposed people eventually become infectious.\n",
        "* $I^u$: Number of people in each city who are infectious but undocumented.  In the model, this actually means \"will never be documented\".\n",
        "* $I^r$: Number of people in each city who are infectious and documented as such.  Li et al model reporting delays, so $I^r$ actually corresponds to something like \"case is severe enough to be documented at some point in the future\".\n",
        "\n",
        "As we will see below, we will be inferring these states by running an Ensemble-adjusted Kalman Filter (EAKF) forward in time.  The state vector of the EAKF is one city-indexed vector for each of these quantities.\n",
        "\n",
        "The model has the following inferrable global, time-invariant parameters:\n",
        "\n",
        "* $\\beta$: The transmission rate due to documented-infectious individuals.\n",
        "* $\\mu$: The relative transmission rate due to undocumented-infectious\n",
        "  individuals. This will act through the product $\\mu \\beta$.\n",
        "* $\\theta$: The intercity mobility factor. This is a factor greater than\n",
        "  1 correcting for underreporting of mobility data (and for population growth\n",
        "  from 2018 to 2020).\n",
        "* $Z$: The average incubation period (i.e., time in the \"exposed\" state).\n",
        "* $\\alpha$: This is the fraction of infections severe enough to be (eventually) documented.\n",
        "* $D$: The average duration of infections (i.e., time in either \"infectious\" state).\n",
        "\n",
        "We will be inferring point estimates for these parameters with an Iterative-Filtering loop around the EAKF for the states.\n",
        "\n",
        "The model also depends on un-inferred constants:\n",
        "* $M$: The intercity mobility matrix.  This is time-varying and presumed given.  Recall that it's scaled by the inferred parameter $\\theta$ to give the actual population movements between cities.\n",
        "* $N$: The total number of people in each city.  The initial populations are taken as given, and the time-variation of population is computed from the mobility numbers $\\theta M$.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "--4jYF-Q9maG"
      },
      "source": [
        "First, we give ourselves some data structures for holding our states and parameters.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "VacihFdC25l4"
      },
      "outputs": [],
      "source": [
        "SEIRComponents = collections.namedtuple(\n",
        "  typename='SEIRComponents',\n",
        "  field_names=[\n",
        "    'susceptible',              # S\n",
        "    'exposed',                  # E\n",
        "    'documented_infectious',    # I^r\n",
        "    'undocumented_infectious',  # I^u\n",
        "    # This is the count of new cases in the \"documented infectious\" compartment.\n",
        "    # We need this because we will introduce a reporting delay, between a person\n",
        "    # entering I^r and showing up in the observable case count data.\n",
        "    # This can't be computed from the cumulative `documented_infectious` count,\n",
        "    # because some portion of that population will move to the 'recovered'\n",
        "    # state, which we aren't tracking explicitly.\n",
        "    'daily_new_documented_infectious'])\n",
        "\n",
        "ModelParams = collections.namedtuple(\n",
        "    typename='ModelParams',\n",
        "    field_names=[\n",
        "      'documented_infectious_tx_rate',             # Beta\n",
        "      'undocumented_infectious_tx_relative_rate',  # Mu\n",
        "      'intercity_underreporting_factor',           # Theta\n",
        "      'average_latency_period',                    # Z\n",
        "      'fraction_of_documented_infections',         # Alpha\n",
        "      'average_infection_duration'                 # D\n",
        "    ]\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kBgUMzTL_2gc"
      },
      "source": [
        "We also code Li et al's bounds for the values of the parameters."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "H_HWdcXZ_1Cw"
      },
      "outputs": [],
      "source": [
        "PARAMETER_LOWER_BOUNDS = ModelParams(\n",
        "    documented_infectious_tx_rate=0.8,\n",
        "    undocumented_infectious_tx_relative_rate=0.2,\n",
        "    intercity_underreporting_factor=1.,\n",
        "    average_latency_period=2.,\n",
        "    fraction_of_documented_infections=0.02,\n",
        "    average_infection_duration=2.\n",
        ")\n",
        "\n",
        "PARAMETER_UPPER_BOUNDS = ModelParams(\n",
        "    documented_infectious_tx_rate=1.5,\n",
        "    undocumented_infectious_tx_relative_rate=1.,\n",
        "    intercity_underreporting_factor=1.75,\n",
        "    average_latency_period=5.,\n",
        "    fraction_of_documented_infections=1.,\n",
        "    average_infection_duration=5.\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-yizvLfw-CiT"
      },
      "source": [
        "## SEIR Dynamics\n",
        "\n",
        "Here we define the relationship between the parameters and state.\n",
        "\n",
        "The time-dynamics equations from Li et al (supplemental material, eqns 1-5) are as follows:\n",
        "\n",
        "$\\frac{dS_i}{dt} = -\\beta \\frac{S_i I_i^r}{N_i} - \\mu \\beta \\frac{S_i I_i^u}{N_i} + \\theta \\sum_k \\frac{M_{ij} S_j}{N_j - I_j^r} - + \\theta \\sum_k \\frac{M_{ji} S_j}{N_i - I_i^r}$\n",
        "\n",
        "$\\frac{dE_i}{dt} = \\beta \\frac{S_i I_i^r}{N_i} + \\mu \\beta \\frac{S_i I_i^u}{N_i} -\\frac{E_i}{Z} + \\theta \\sum_k \\frac{M_{ij} E_j}{N_j - I_j^r} - + \\theta \\sum_k \\frac{M_{ji} E_j}{N_i - I_i^r}$\n",
        "\n",
        "$\\frac{dI^r_i}{dt} = \\alpha \\frac{E_i}{Z} - \\frac{I_i^r}{D}$\n",
        "\n",
        "$\\frac{dI^u_i}{dt} = (1 - \\alpha) \\frac{E_i}{Z} - \\frac{I_i^u}{D} + \\theta \\sum_k \\frac{M_{ij} I_j^u}{N_j - I_j^r} - + \\theta \\sum_k \\frac{M_{ji} I^u_j}{N_i - I_i^r}$\n",
        "\n",
        "$N_i = N_i + \\theta \\sum_j M_{ij} - \\theta \\sum_j M_{ji}$\n",
        "\n",
        "As a reminder, the $i$ and $j$ subscripts index cities.  These equations model the time-evolution of the disease through\n",
        "- Contact with infectious individuals leading to more infection;\n",
        "- Disease progression from \"exposed\" to one of the \"infectious\" states;\n",
        "- Disease progression from \"infectious\" states to recovery, which we model by removal from the modeled population;\n",
        "- Inter-city mobility, including exposed or undocumented-infectious persons; and\n",
        "- Time-variation of daily city populations through inter-city mobility.\n",
        "\n",
        "Following Li et al, we assume that people with cases severe enough to eventually be reported do not travel between cities.\n",
        "\n",
        "Also following Li et al, we treat these dynamics as subject to term-wise Poisson noise, i.e., each term is actually the rate of a Poisson, a sample from which gives the true change.  The Poisson noise is term-wise because subtracting (as opposed to adding) Poisson samples does not yield a Poisson-distributed result.\n",
        "\n",
        "We will evolve these dynamics forward in time with the classic fourth-order Runge-Kutta integrator, but first let's define the function that computes them (including sampling the Poisson noise)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_Cpj5Lyo-AGw"
      },
      "outputs": [],
      "source": [
        "def sample_state_deltas(\n",
        "    state, population, mobility_matrix, params, seed, is_deterministic=False):\n",
        "  \"\"\"Computes one-step change in state, including Poisson sampling.\n",
        "  \n",
        "  Note that this is coded to support vectorized evaluation on arbitrary-shape\n",
        "  batches of states.  This is useful, for example, for running multiple\n",
        "  independent replicas of this model to compute credible intervals for the\n",
        "  parameters.  We refer to the arbitrary batch shape with the conventional\n",
        "  `B` in the parameter documentation below.  This function also, of course,\n",
        "  supports broadcasting over the batch shape.\n",
        "\n",
        "  Args:\n",
        "    state: A `SEIRComponents` tuple with fields Tensors of shape\n",
        "      B + [num_locations] giving the current disease state.\n",
        "    population: A Tensor of shape B + [num_locations] giving the current city\n",
        "      populations.\n",
        "    mobility_matrix: A Tensor of shape B + [num_locations, num_locations] giving\n",
        "      the current baseline inter-city mobility.\n",
        "    params: A `ModelParams` tuple with fields Tensors of shape B giving the\n",
        "      global parameters for the current EAKF run.\n",
        "    seed: Initial entropy for pseudo-random number generation.  The Poisson\n",
        "      sampling is repeatable by supplying the same seed.\n",
        "    is_deterministic: A `bool` flag to turn off Poisson sampling if desired.\n",
        "\n",
        "  Returns:\n",
        "    delta: A `SEIRComponents` tuple with fields Tensors of shape\n",
        "      B + [num_locations] giving the one-day changes in the state, according\n",
        "      to equations 1-4 above (including Poisson noise per Li et al).\n",
        "  \"\"\"\n",
        "  undocumented_infectious_fraction = state.undocumented_infectious / population\n",
        "  documented_infectious_fraction = state.documented_infectious / population\n",
        "\n",
        "  # Anyone not documented as infectious is considered mobile\n",
        "  mobile_population = (population - state.documented_infectious)\n",
        "  def compute_outflow(compartment_population):\n",
        "    raw_mobility = tf.linalg.matvec(\n",
        "        mobility_matrix, compartment_population / mobile_population)\n",
        "    return params.intercity_underreporting_factor * raw_mobility\n",
        "  def compute_inflow(compartment_population):\n",
        "    raw_mobility = tf.linalg.matmul(\n",
        "        mobility_matrix,\n",
        "        (compartment_population / mobile_population)[..., tf.newaxis],\n",
        "        transpose_a=True)\n",
        "    return params.intercity_underreporting_factor * tf.squeeze(\n",
        "        raw_mobility, axis=-1)\n",
        "\n",
        "  # Helper for sampling the Poisson-variate terms.\n",
        "  seeds = samplers.split_seed(seed, n=11)\n",
        "  if is_deterministic:\n",
        "    def sample_poisson(rate):\n",
        "      return rate\n",
        "  else:\n",
        "    def sample_poisson(rate):\n",
        "      return tfd.Poisson(rate=rate).sample(seed=seeds.pop())\n",
        "\n",
        "  # Below are the various terms called U1-U12 in the paper. We combined the\n",
        "  # first two, which should be fine; both are poisson so their sum is too, and\n",
        "  # there's no risk (as there could be in other terms) of going negative.\n",
        "  susceptible_becoming_exposed = sample_poisson(\n",
        "      state.susceptible *\n",
        "      (params.documented_infectious_tx_rate *\n",
        "       documented_infectious_fraction +\n",
        "       (params.undocumented_infectious_tx_relative_rate *\n",
        "        params.documented_infectious_tx_rate) *\n",
        "       undocumented_infectious_fraction))  # U1 + U2\n",
        "\n",
        "  susceptible_population_inflow = sample_poisson(\n",
        "      compute_inflow(state.susceptible))  # U3\n",
        "  susceptible_population_outflow = sample_poisson(\n",
        "      compute_outflow(state.susceptible))  # U4\n",
        "\n",
        "  exposed_becoming_documented_infectious = sample_poisson(\n",
        "      params.fraction_of_documented_infections *\n",
        "      state.exposed / params.average_latency_period)  # U5\n",
        "  exposed_becoming_undocumented_infectious = sample_poisson(\n",
        "      (1 - params.fraction_of_documented_infections) *\n",
        "      state.exposed / params.average_latency_period)  # U6\n",
        "\n",
        "  exposed_population_inflow = sample_poisson(\n",
        "      compute_inflow(state.exposed))  # U7\n",
        "  exposed_population_outflow = sample_poisson(\n",
        "      compute_outflow(state.exposed))  # U8\n",
        "\n",
        "  documented_infectious_becoming_recovered = sample_poisson(\n",
        "      state.documented_infectious /\n",
        "      params.average_infection_duration)  # U9\n",
        "  undocumented_infectious_becoming_recovered = sample_poisson(\n",
        "      state.undocumented_infectious /\n",
        "      params.average_infection_duration)  # U10\n",
        "\n",
        "  undocumented_infectious_population_inflow = sample_poisson(\n",
        "      compute_inflow(state.undocumented_infectious))  # U11\n",
        "  undocumented_infectious_population_outflow = sample_poisson(\n",
        "      compute_outflow(state.undocumented_infectious))  # U12\n",
        "\n",
        "  # The final state_deltas\n",
        "  return SEIRComponents(\n",
        "      # Equation [1]\n",
        "      susceptible=(-susceptible_becoming_exposed +\n",
        "                   susceptible_population_inflow +\n",
        "                   -susceptible_population_outflow),\n",
        "      # Equation [2]\n",
        "      exposed=(susceptible_becoming_exposed +\n",
        "               -exposed_becoming_documented_infectious +\n",
        "               -exposed_becoming_undocumented_infectious +\n",
        "               exposed_population_inflow +\n",
        "               -exposed_population_outflow),\n",
        "      # Equation [3]\n",
        "      documented_infectious=(\n",
        "          exposed_becoming_documented_infectious +\n",
        "          -documented_infectious_becoming_recovered),\n",
        "      # Equation [4]\n",
        "      undocumented_infectious=(\n",
        "          exposed_becoming_undocumented_infectious +\n",
        "          -undocumented_infectious_becoming_recovered +\n",
        "          undocumented_infectious_population_inflow +\n",
        "          -undocumented_infectious_population_outflow),\n",
        "      # New to-be-documented infectious cases, subject to the delayed\n",
        "      # observation model.\n",
        "      daily_new_documented_infectious=exposed_becoming_documented_infectious)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K7T_QQTRKqOE"
      },
      "source": [
        "Here's the integrator.  This is completely standard, except for passing the PRNG seed through to the `sample_state_deltas` function to get independent Poisson noise at each of the partial steps that the Runge-Kutta method calls for."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "2qx4tX8sCAZv"
      },
      "outputs": [],
      "source": [
        "@tf.function(autograph=False)\n",
        "def rk4_one_step(state, population, mobility_matrix, params, seed):\n",
        "  \"\"\"Implement one step of RK4, wrapped around a call to sample_state_deltas.\"\"\"\n",
        "  # One seed for each RK sub-step\n",
        "  seeds = samplers.split_seed(seed, n=4)\n",
        "\n",
        "  deltas = tf.nest.map_structure(tf.zeros_like, state)\n",
        "  combined_deltas = tf.nest.map_structure(tf.zeros_like, state)\n",
        "\n",
        "  for a, b in zip([1., 2, 2, 1.], [6., 3., 3., 6.]):\n",
        "    next_input = tf.nest.map_structure(\n",
        "        lambda x, delta, a=a: x + delta / a, state, deltas)\n",
        "    deltas = sample_state_deltas(\n",
        "        next_input,\n",
        "        population,\n",
        "        mobility_matrix,\n",
        "        params,\n",
        "        seed=seeds.pop(), is_deterministic=False)\n",
        "    combined_deltas = tf.nest.map_structure(\n",
        "        lambda x, delta, b=b: x + delta / b, combined_deltas, deltas)\n",
        "\n",
        "  return tf.nest.map_structure(\n",
        "      lambda s, delta: s + tf.round(delta),\n",
        "      state, combined_deltas)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3gVKuTqi32Bn"
      },
      "source": [
        "## Initialization\n",
        "  \n",
        "Here we implement the initialization scheme from the paper.\n",
        "\n",
        "Following Li et al, our inference scheme will be an ensemble adjustment Kalman filter inner loop, surrounded by an iterated filtering outer loop (IF-EAKF).  Computationally, that means we need three kinds of initialization:\n",
        "- Initial state for the inner EAKF\n",
        "- Initial parameters for the outer IF, which are also the initial\n",
        "  parameters for the first EAKF\n",
        "- Updating parameters from one IF iteration to the next, which serve\n",
        "  as the initial parameters for each EAKF other than the first.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "rdRf_UmdvPLo"
      },
      "outputs": [],
      "source": [
        "def initialize_state(num_particles, num_batches, seed):\n",
        "  \"\"\"Initialize the state for a batch of EAKF runs.\n",
        "  \n",
        "  Args:\n",
        "    num_particles: `int` giving the number of particles for the EAKF.\n",
        "    num_batches: `int` giving the number of independent EAKF runs to\n",
        "      initialize in a vectorized batch.\n",
        "    seed: PRNG entropy.\n",
        "    \n",
        "  Returns:\n",
        "    state: A `SEIRComponents` tuple with Tensors of shape [num_particles,\n",
        "      num_batches, num_cities] giving the initial conditions in each\n",
        "      city, in each filter particle, in each batch member.\n",
        "  \"\"\"\n",
        "  num_cities = mobility_matrix_over_time.shape[-2]\n",
        "  state_shape = [num_particles, num_batches, num_cities]\n",
        "  susceptible = initial_population * np.ones(state_shape, dtype=np.float32)\n",
        "  documented_infectious = np.zeros(state_shape, dtype=np.float32)\n",
        "  daily_new_documented_infectious = np.zeros(state_shape, dtype=np.float32)\n",
        "\n",
        "  # Following Li et al, initialize Wuhan with up to 2000 people exposed\n",
        "  # and another up to 2000 undocumented infectious.\n",
        "  rng = np.random.RandomState(seed[0] % (2**31 - 1))\n",
        "  wuhan_exposed = rng.randint(\n",
        "      0, 2001, [num_particles, num_batches]).astype(np.float32)\n",
        "  wuhan_undocumented_infectious = rng.randint(\n",
        "      0, 2001, [num_particles, num_batches]).astype(np.float32)\n",
        " \n",
        "  # Also following Li et al, initialize cities adjacent to Wuhan with three\n",
        "  # days' worth of additional exposed and undocumented-infectious cases,\n",
        "  # as they may have traveled there before the beginning of the modeling\n",
        "  # period.\n",
        "  exposed = 3 * mobility_matrix_over_time[\n",
        "      WUHAN_IDX, :, 0] * wuhan_exposed[\n",
        "          ..., np.newaxis] / initial_population[WUHAN_IDX]\n",
        "  undocumented_infectious = 3 * mobility_matrix_over_time[\n",
        "      WUHAN_IDX, :, 0] * wuhan_undocumented_infectious[\n",
        "          ..., np.newaxis] / initial_population[WUHAN_IDX]\n",
        "\n",
        "  exposed[..., WUHAN_IDX] = wuhan_exposed\n",
        "  undocumented_infectious[..., WUHAN_IDX] = wuhan_undocumented_infectious\n",
        "\n",
        "  # Following Li et al, we do not remove the inital exposed and infectious\n",
        "  # persons from the susceptible population.\n",
        "  return SEIRComponents(\n",
        "      susceptible=tf.constant(susceptible),\n",
        "      exposed=tf.constant(exposed),\n",
        "      documented_infectious=tf.constant(documented_infectious),\n",
        "      undocumented_infectious=tf.constant(undocumented_infectious),\n",
        "      daily_new_documented_infectious=tf.constant(daily_new_documented_infectious))\n",
        "  \n",
        "def initialize_params(num_particles, num_batches, seed):\n",
        "  \"\"\"Initialize the global parameters for the entire inference run.\n",
        "\n",
        "  Args:\n",
        "    num_particles: `int` giving the number of particles for the EAKF.\n",
        "    num_batches: `int` giving the number of independent EAKF runs to\n",
        "      initialize in a vectorized batch.\n",
        "    seed: PRNG entropy.\n",
        "    \n",
        "  Returns:\n",
        "    params: A `ModelParams` tuple with fields Tensors of shape\n",
        "      [num_particles, num_batches] giving the global parameters\n",
        "      to use for the first batch of EAKF runs.\n",
        "  \"\"\"\n",
        "  # We have 6 parameters. We'll initialize with a Sobol sequence,\n",
        "  # covering the hyper-rectangle defined by our parameter limits.\n",
        "  halton_sequence = tfp.mcmc.sample_halton_sequence(\n",
        "      dim=6, num_results=num_particles * num_batches, seed=seed)\n",
        "  halton_sequence = tf.reshape(\n",
        "      halton_sequence, [num_particles, num_batches, 6])\n",
        "  halton_sequences = tf.nest.pack_sequence_as(\n",
        "      PARAMETER_LOWER_BOUNDS, tf.split(\n",
        "          halton_sequence, num_or_size_splits=6, axis=-1))\n",
        "  def interpolate(minval, maxval, h):\n",
        "    return (maxval - minval) * h + minval\n",
        "  return tf.nest.map_structure(\n",
        "      interpolate,\n",
        "      PARAMETER_LOWER_BOUNDS, PARAMETER_UPPER_BOUNDS, halton_sequences)\n",
        "\n",
        "def update_params(num_particles, num_batches,\n",
        "                  prev_params, parameter_variance, seed):\n",
        "  \"\"\"Update the global parameters between EAKF runs.\n",
        "\n",
        "  Args:\n",
        "    num_particles: `int` giving the number of particles for the EAKF.\n",
        "    num_batches: `int` giving the number of independent EAKF runs to\n",
        "      initialize in a vectorized batch.\n",
        "    prev_params: A `ModelParams` tuple of the parameters used for the previous\n",
        "      EAKF run.\n",
        "    parameter_variance: A `ModelParams` tuple specifying how much to drift\n",
        "      each parameter.\n",
        "    seed: PRNG entropy.\n",
        "    \n",
        "  Returns:\n",
        "    params: A `ModelParams` tuple with fields Tensors of shape\n",
        "      [num_particles, num_batches] giving the global parameters\n",
        "      to use for the next batch of EAKF runs.\n",
        "  \"\"\"\n",
        "  # Initialize near the previous set of parameters. This is the first step\n",
        "  # in Iterated Filtering.\n",
        "  seeds = tf.nest.pack_sequence_as(\n",
        "      prev_params, samplers.split_seed(seed, n=len(prev_params)))\n",
        "  return tf.nest.map_structure(\n",
        "      lambda x, v, seed: x + tf.math.sqrt(v) * tf.random.stateless_normal([\n",
        "          num_particles, num_batches, 1], seed=seed),\n",
        "      prev_params, parameter_variance, seeds)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jKWm64gF0JkZ"
      },
      "source": [
        "## Delays\n",
        "\n",
        "One of the important features of this model is taking explicit account of the fact that infections are reported later than they begin.  That is, we expect that a person who moves from the $E$ compartment to the $I^r$ compartment on day $t$ may not show up in the observable reported case counts until some later day.\n",
        "\n",
        "We assume the delay is gamma-distributed.  Following Li et al, we use 1.85 for the shape, and parameterize the rate to produce an average reporting delay of 9 days."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "rFNy6L491BFD"
      },
      "outputs": [],
      "source": [
        "def raw_reporting_delay_distribution(gamma_shape=1.85, reporting_delay=9.):\n",
        "  return tfp.distributions.Gamma(\n",
        "      concentration=gamma_shape, rate=gamma_shape / reporting_delay)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yQTwUeKr8dVP"
      },
      "source": [
        "Our observations are discrete, so we will round the raw (continuous) delays up to the nearest day.  We also have a finite data horizon, so the delay distribution for a single person is a categorical over the remaining days.  We can therefore compute the per-city predicted observations more efficiently than sampling $O(I^r)$ gammas, by pre-computing multinomial delay probabilities instead."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0YRv0FjX9DfB"
      },
      "outputs": [],
      "source": [
        "def reporting_delay_probs(num_timesteps, gamma_shape=1.85, reporting_delay=9.):\n",
        "  gamma_dist = raw_reporting_delay_distribution(gamma_shape, reporting_delay)\n",
        "  multinomial_probs = [gamma_dist.cdf(1.)]\n",
        "  for k in range(2, num_timesteps + 1):\n",
        "    multinomial_probs.append(gamma_dist.cdf(k) - gamma_dist.cdf(k - 1))\n",
        "  # For samples that are larger than T.\n",
        "  multinomial_probs.append(gamma_dist.survival_function(num_timesteps))\n",
        "  multinomial_probs = tf.stack(multinomial_probs)\n",
        "  return multinomial_probs"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7WAHi68lBFqz"
      },
      "source": [
        "Here's the code for actually applying these delays to the new daily documented infectious counts:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "vrPHDvUEBPsS"
      },
      "outputs": [],
      "source": [
        "def delay_reporting(\n",
        "    daily_new_documented_infectious, num_timesteps, t, multinomial_probs, seed):\n",
        "  # This is the distribution of observed infectious counts from the current\n",
        "  # timestep.\n",
        "\n",
        "  raw_delays = tfd.Multinomial(\n",
        "      total_count=daily_new_documented_infectious,\n",
        "      probs=multinomial_probs).sample(seed=seed)\n",
        "\n",
        "  # The last bucket is used for samples that are out of range of T + 1. Thus\n",
        "  # they are not going to be observable in this model.\n",
        "  clipped_delays = raw_delays[..., :-1]\n",
        "\n",
        "  # We can also remove counts that are such that t + i >= T.\n",
        "  clipped_delays = clipped_delays[..., :num_timesteps - t]\n",
        "  # We finally shift everything by t. That means prepending with zeros.\n",
        "  return tf.concat([\n",
        "      tf.zeros(\n",
        "          tf.concat([\n",
        "              tf.shape(clipped_delays)[:-1], [t]], axis=0),\n",
        "          dtype=clipped_delays.dtype),\n",
        "      clipped_delays], axis=-1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DRsd3wsW9WYQ"
      },
      "source": [
        "## Inference"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2lO5MVT6M2lc"
      },
      "source": [
        "First we'll define some data structures for inference.\n",
        "\n",
        "In particular, we'll be wanting to do Iterated Filtering, which packages the\n",
        "state and parameters together while doing inference. So we'll define\n",
        "a `ParameterStatePair` object.\n",
        "\n",
        "We also want to package any side information to the model."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6JrCjAhXM6TL"
      },
      "outputs": [],
      "source": [
        "ParameterStatePair = collections.namedtuple(\n",
        "    'ParameterStatePair', ['state', 'params'])\n",
        "\n",
        "# Info that is tracked and mutated but should not have inference performed over.\n",
        "SideInfo = collections.namedtuple(\n",
        "    'SideInfo', [\n",
        "        # Observations at every time step.\n",
        "        'observations_over_time',\n",
        "        'initial_population',\n",
        "        'mobility_matrix_over_time',\n",
        "        'population',\n",
        "        # Used for variance of measured observations.\n",
        "        'actual_reported_cases',\n",
        "        # Pre-computed buckets for the multinomial distribution.\n",
        "        'multinomial_probs',\n",
        "        'seed',\n",
        "    ])\n",
        "\n",
        "# Cities can not fall below this fraction of people\n",
        "MINIMUM_CITY_FRACTION = 0.6\n",
        "\n",
        "# How much to inflate the covariance by.\n",
        "INFLATION_FACTOR = 1.1\n",
        "\n",
        "INFLATE_FN = tfes.inflate_by_scaled_identity_fn(INFLATION_FACTOR)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eoZPQ9YDM9mj"
      },
      "source": [
        "Here is the complete observation model, packaged for the Ensemble Kalman Filter.\n",
        "\n",
        "The interesting feature is the reporting delays (computed as previously).  The upstream model emits the `daily_new_documented_infectious` for each city at each time step."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lBrt1BkO9Xje"
      },
      "outputs": [],
      "source": [
        "# We observe the observed infections.\n",
        "def observation_fn(t, state_params, extra):\n",
        "  \"\"\"Generate reported cases.\n",
        "  \n",
        "  Args:\n",
        "    state_params: A `ParameterStatePair` giving the current parameters\n",
        "      and state.\n",
        "    t: Integer giving the current time.\n",
        "    extra: A `SideInfo` carrying auxiliary information.\n",
        "\n",
        "  Returns:\n",
        "    observations: A Tensor of predicted observables, namely new cases\n",
        "      per city at time `t`.\n",
        "    extra: Update `SideInfo`.\n",
        "  \"\"\"\n",
        "  # Undo padding introduced in `inference`.\n",
        "  daily_new_documented_infectious = state_params.state.daily_new_documented_infectious[..., 0]\n",
        "  # Number of people that we have already committed to become\n",
        "  # observed infectious over time.\n",
        "  # shape: batch + [num_particles, num_cities, time]\n",
        "  observations_over_time = extra.observations_over_time\n",
        "  num_timesteps = observations_over_time.shape[-1]\n",
        "\n",
        "  seed, new_seed = samplers.split_seed(extra.seed, salt='reporting delay')\n",
        "  \n",
        "  daily_delayed_counts = delay_reporting(\n",
        "      daily_new_documented_infectious, num_timesteps, t,\n",
        "      extra.multinomial_probs, seed)\n",
        "  observations_over_time = observations_over_time + daily_delayed_counts\n",
        "\n",
        "  extra = extra._replace(\n",
        "      observations_over_time=observations_over_time,\n",
        "      seed=new_seed)\n",
        "\n",
        "  # Actual predicted new cases, re-padded.\n",
        "  adjusted_observations = observations_over_time[..., t][..., tf.newaxis]\n",
        "  # Finally observations have variance that is a function of the true observations:\n",
        "  return tfd.MultivariateNormalDiag(\n",
        "      loc=adjusted_observations,\n",
        "      scale_diag=tf.math.maximum(\n",
        "          2., extra.actual_reported_cases[..., t][..., tf.newaxis] / 2.)), extra"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ugNrSlDAyUc6"
      },
      "source": [
        "Here we define the transition dynamics. We've done the semantic work already; here we just package it for the EAKF framework, and, following Li et al, clip city populations to prevent them from getting too small."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "95S7LAj4NB_5"
      },
      "outputs": [],
      "source": [
        "def transition_fn(t, state_params, extra):\n",
        "  \"\"\"SEIR dynamics.\n",
        "\n",
        "  Args:\n",
        "    state_params: A `ParameterStatePair` giving the current parameters\n",
        "      and state.\n",
        "    t: Integer giving the current time.\n",
        "    extra: A `SideInfo` carrying auxiliary information.\n",
        "\n",
        "  Returns:\n",
        "    state_params: A `ParameterStatePair` predicted for the next time step.\n",
        "    extra: Updated `SideInfo`.\n",
        "  \"\"\"\n",
        "  mobility_t = extra.mobility_matrix_over_time[..., t]\n",
        "  new_seed, rk4_seed = samplers.split_seed(extra.seed, salt='Transition')\n",
        "  new_state = rk4_one_step(\n",
        "      state_params.state,\n",
        "      extra.population,\n",
        "      mobility_t,\n",
        "      state_params.params,\n",
        "      seed=rk4_seed)\n",
        "\n",
        "  # Make sure population doesn't go below MINIMUM_CITY_FRACTION.\n",
        "  new_population = (\n",
        "      extra.population + state_params.params.intercity_underreporting_factor * (\n",
        "          # Inflow\n",
        "          tf.reduce_sum(mobility_t, axis=-2) - \n",
        "          # Outflow\n",
        "          tf.reduce_sum(mobility_t, axis=-1)))\n",
        "  new_population = tf.where(\n",
        "      new_population < MINIMUM_CITY_FRACTION * extra.initial_population,\n",
        "      extra.initial_population * MINIMUM_CITY_FRACTION,\n",
        "      new_population)\n",
        "\n",
        "  extra = extra._replace(population=new_population, seed=new_seed)\n",
        "\n",
        "  # The Ensemble Kalman Filter code expects the transition function to return a distribution.\n",
        "  # As the dynamics and noise are encapsulated above, we construct a `JointDistribution` that when\n",
        "  # sampled, returns the values above.\n",
        "\n",
        "  new_state = tfd.JointDistributionNamed(\n",
        "      model=tf.nest.map_structure(lambda x: tfd.VectorDeterministic(x), new_state))\n",
        "  params = tfd.JointDistributionNamed(\n",
        "      model=tf.nest.map_structure(lambda x: tfd.VectorDeterministic(x), state_params.params))\n",
        "  \n",
        "  state_params = tfd.JointDistributionNamed(\n",
        "      model=ParameterStatePair(state=new_state, params=params))\n",
        "\n",
        "  return state_params, extra"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nsdNsvzuyaN-"
      },
      "source": [
        "Finally we define the inference method. This is two loops, the outer loop\n",
        "being Iterated Filtering while the inner loop is Ensemble Adjustment Kalman Filtering."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "EUWinMkUNFGJ"
      },
      "outputs": [],
      "source": [
        "# Use tf.function to speed up EAKF prediction and updates.\n",
        "ensemble_kalman_filter_predict = tf.function(\n",
        "    tfes.ensemble_kalman_filter_predict, autograph=False)\n",
        "ensemble_adjustment_kalman_filter_update = tf.function(\n",
        "    tfes.ensemble_adjustment_kalman_filter_update, autograph=False)\n",
        "\n",
        "def inference(\n",
        "    num_ensembles,\n",
        "    num_batches,\n",
        "    num_iterations,\n",
        "    actual_reported_cases,\n",
        "    mobility_matrix_over_time,\n",
        "    seed=None,\n",
        "    # This is how much to reduce the variance by in every iterative\n",
        "    # filtering step.\n",
        "    variance_shrinkage_factor=0.9,\n",
        "    # Days before infection is reported.\n",
        "    reporting_delay=9.,\n",
        "    # Shape parameter of Gamma distribution.\n",
        "    gamma_shape_parameter=1.85):\n",
        "  \"\"\"Inference for the Shaman, et al. model.\n",
        "\n",
        "  Args:\n",
        "    num_ensembles: Number of particles to use for EAKF.\n",
        "    num_batches: Number of batches of IF-EAKF to run.\n",
        "    num_iterations: Number of iterations to run iterative filtering.\n",
        "    actual_reported_cases: `Tensor` of shape `[L, T]` where `L` is the number\n",
        "      of cities, and `T` is the timesteps.\n",
        "    mobility_matrix_over_time: `Tensor` of shape `[L, L, T]` which specifies the\n",
        "      mobility between locations over time.\n",
        "    variance_shrinkage_factor: Python `float`. How much to reduce the\n",
        "      variance each iteration of iterated filtering.\n",
        "    reporting_delay: Python `float`. How many days before the infection\n",
        "      is reported.\n",
        "    gamma_shape_parameter: Python `float`. Shape parameter of Gamma distribution\n",
        "      of reporting delays.\n",
        "\n",
        "  Returns:\n",
        "    result: A `ModelParams` with fields Tensors of shape [num_batches],\n",
        "      containing the inferred parameters at the final iteration.\n",
        "  \"\"\"\n",
        "  print('Starting inference.')\n",
        "  num_timesteps = actual_reported_cases.shape[-1]\n",
        "  params_per_iter = []\n",
        "\n",
        "  multinomial_probs = reporting_delay_probs(\n",
        "      num_timesteps, gamma_shape_parameter, reporting_delay)\n",
        "\n",
        "  seed = samplers.sanitize_seed(seed, salt='Inference')\n",
        "\n",
        "  for i in range(num_iterations):\n",
        "    start_if_time = time.time()\n",
        "    seeds = samplers.split_seed(seed, n=4, salt='Initialize')\n",
        "    if params_per_iter:\n",
        "      parameter_variance = tf.nest.map_structure(\n",
        "          lambda minval, maxval: variance_shrinkage_factor ** (\n",
        "              2 * i) * (maxval - minval) ** 2 / 4.,\n",
        "          PARAMETER_LOWER_BOUNDS, PARAMETER_UPPER_BOUNDS)\n",
        "      params_t = update_params(\n",
        "          num_ensembles,\n",
        "          num_batches,\n",
        "          prev_params=params_per_iter[-1],\n",
        "          parameter_variance=parameter_variance,\n",
        "          seed=seeds.pop())\n",
        "    else:\n",
        "      params_t = initialize_params(num_ensembles, num_batches, seed=seeds.pop())\n",
        "\n",
        "    state_t = initialize_state(num_ensembles, num_batches, seed=seeds.pop())\n",
        "    population_t = sum(x for x in state_t)\n",
        "    observations_over_time = tf.zeros(\n",
        "        [num_ensembles,\n",
        "         num_batches,\n",
        "         actual_reported_cases.shape[0], num_timesteps])\n",
        "\n",
        "    extra = SideInfo(\n",
        "        observations_over_time=observations_over_time,\n",
        "        initial_population=tf.identity(population_t),\n",
        "        mobility_matrix_over_time=mobility_matrix_over_time,\n",
        "        population=population_t,\n",
        "        multinomial_probs=multinomial_probs,\n",
        "        actual_reported_cases=actual_reported_cases,\n",
        "        seed=seeds.pop())\n",
        "\n",
        "    # Clip states\n",
        "    state_t = clip_state(state_t, population_t)\n",
        "    params_t = clip_params(params_t, seed=seeds.pop())\n",
        "\n",
        "    # Accrue the parameter over time. We'll be averaging that\n",
        "    # and using that as our MLE estimate.\n",
        "    params_over_time = tf.nest.map_structure(\n",
        "        lambda x: tf.identity(x), params_t)\n",
        "\n",
        "    state_params = ParameterStatePair(state=state_t, params=params_t)\n",
        "\n",
        "    eakf_state = tfes.EnsembleKalmanFilterState(\n",
        "        step=tf.constant(0), particles=state_params, extra=extra)\n",
        "\n",
        "    for j in range(num_timesteps):\n",
        "      seeds = samplers.split_seed(eakf_state.extra.seed, n=3)\n",
        "      \n",
        "      extra = extra._replace(seed=seeds.pop())\n",
        "    \n",
        "      # Predict step.\n",
        "\n",
        "      # Inflate and clip.\n",
        "      new_particles = INFLATE_FN(eakf_state.particles)\n",
        "      state_t = clip_state(new_particles.state, eakf_state.extra.population)\n",
        "      params_t = clip_params(new_particles.params, seed=seeds.pop())\n",
        "      eakf_state = eakf_state._replace(\n",
        "          particles=ParameterStatePair(params=params_t, state=state_t))\n",
        "\n",
        "      eakf_predict_state = ensemble_kalman_filter_predict(eakf_state, transition_fn)\n",
        "\n",
        "      # Clip the state and particles.\n",
        "      state_params = eakf_predict_state.particles\n",
        "      state_t = clip_state(\n",
        "          state_params.state, eakf_predict_state.extra.population)\n",
        "      state_params = ParameterStatePair(state=state_t, params=state_params.params)\n",
        "\n",
        "      # We preprocess the state and parameters by affixing a 1 dimension. This is because for\n",
        "      # inference, we treat each city as independent. We could also introduce localization by\n",
        "      # considering cities that are adjacent.\n",
        "      state_params = tf.nest.map_structure(lambda x: x[..., tf.newaxis], state_params)\n",
        "      eakf_predict_state = eakf_predict_state._replace(particles=state_params)\n",
        "\n",
        "      # Update step.\n",
        "      \n",
        "      eakf_update_state = ensemble_adjustment_kalman_filter_update(\n",
        "          eakf_predict_state,\n",
        "          actual_reported_cases[..., j][..., tf.newaxis],\n",
        "          observation_fn)\n",
        "      \n",
        "      state_params = tf.nest.map_structure(\n",
        "          lambda x: x[..., 0], eakf_update_state.particles)\n",
        "\n",
        "      # Clip to ensure parameters / state are well constrained.\n",
        "      state_t = clip_state(\n",
        "          state_params.state, eakf_update_state.extra.population)\n",
        "      \n",
        "      # Finally for the parameters, we should reduce over all updates. We get\n",
        "      # an extra dimension back so let's do that.\n",
        "      params_t = tf.nest.map_structure(\n",
        "          lambda x, y: x + tf.reduce_sum(y[..., tf.newaxis] - x, axis=-2, keepdims=True),\n",
        "          eakf_predict_state.particles.params, state_params.params)\n",
        "      params_t = clip_params(params_t, seed=seeds.pop())\n",
        "      params_t = tf.nest.map_structure(lambda x: x[..., 0], params_t)\n",
        "\n",
        "      state_params = ParameterStatePair(state=state_t, params=params_t)\n",
        "      eakf_state = eakf_update_state\n",
        "      eakf_state = eakf_state._replace(particles=state_params)\n",
        "\n",
        "      # Flatten and collect the inferred parameter at time step t.\n",
        "      params_over_time = tf.nest.map_structure(\n",
        "          lambda s, x: tf.concat([s, x], axis=-1), params_over_time, params_t)\n",
        "\n",
        "    est_params = tf.nest.map_structure(\n",
        "        # Take the average over the Ensemble and over time.\n",
        "        lambda x: tf.math.reduce_mean(x, axis=[0, -1])[..., tf.newaxis],\n",
        "        params_over_time)\n",
        "    params_per_iter.append(est_params)\n",
        "    print('Iterated Filtering {} / {} Ran in: {:.2f} seconds'.format(\n",
        "        i, num_iterations, time.time() - start_if_time))\n",
        "\n",
        "  return tf.nest.map_structure(\n",
        "      lambda x: tf.squeeze(x, axis=-1), params_per_iter[-1])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UvALK7e1fgKU"
      },
      "source": [
        "Final detail: clipping the parameters and state consists of making sure they are within range, and non-negative."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "aQj7o0nU6-ru"
      },
      "outputs": [],
      "source": [
        "def clip_state(state, population):\n",
        "  \"\"\"Clip state to sensible values.\"\"\"\n",
        "  state = tf.nest.map_structure(\n",
        "      lambda x: tf.where(x < 0, 0., x), state)\n",
        "\n",
        "  # If S > population, then adjust as well.\n",
        "  susceptible = tf.where(state.susceptible > population, population, state.susceptible)\n",
        "  return SEIRComponents(\n",
        "      susceptible=susceptible,\n",
        "      exposed=state.exposed,\n",
        "      documented_infectious=state.documented_infectious,\n",
        "      undocumented_infectious=state.undocumented_infectious,\n",
        "      daily_new_documented_infectious=state.daily_new_documented_infectious)\n",
        "\n",
        "def clip_params(params, seed):\n",
        "  \"\"\"Clip parameters to bounds.\"\"\"\n",
        "  def _clip(p, minval, maxval):\n",
        "    return tf.where(\n",
        "        p < minval,\n",
        "        minval * (1. + 0.1 * tf.random.stateless_uniform(p.shape, seed=seed)),\n",
        "        tf.where(p > maxval,\n",
        "                 maxval * (1. - 0.1 * tf.random.stateless_uniform(\n",
        "                     p.shape, seed=seed)), p))\n",
        "  params = tf.nest.map_structure(\n",
        "      _clip, params, PARAMETER_LOWER_BOUNDS, PARAMETER_UPPER_BOUNDS)\n",
        "\n",
        "  return params"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c7ACJedFAyHQ"
      },
      "source": [
        "## Running it all together"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-T603NTSA0f3"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Starting inference.\n",
            "Iterated Filtering 0 / 10 Ran in: 26.65 seconds\n",
            "Iterated Filtering 1 / 10 Ran in: 28.69 seconds\n",
            "Iterated Filtering 2 / 10 Ran in: 28.06 seconds\n",
            "Iterated Filtering 3 / 10 Ran in: 28.48 seconds\n",
            "Iterated Filtering 4 / 10 Ran in: 28.57 seconds\n",
            "Iterated Filtering 5 / 10 Ran in: 28.35 seconds\n",
            "Iterated Filtering 6 / 10 Ran in: 28.35 seconds\n",
            "Iterated Filtering 7 / 10 Ran in: 28.19 seconds\n",
            "Iterated Filtering 8 / 10 Ran in: 28.58 seconds\n",
            "Iterated Filtering 9 / 10 Ran in: 28.23 seconds\n"
          ]
        }
      ],
      "source": [
        "# Let's sample the parameters.\n",
        "#\n",
        "# NOTE: Li et al. run inference 1000 times, which would take a few hours.\n",
        "# Here we run inference 30 times (in a single, vectorized batch).\n",
        "best_parameters = inference(\n",
        "    num_ensembles=300,\n",
        "    num_batches=30,\n",
        "    num_iterations=10,\n",
        "    actual_reported_cases=observed_daily_infectious_count,\n",
        "    mobility_matrix_over_time=mobility_matrix_over_time)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZWjY1KpJ3JuT"
      },
      "source": [
        "The results of our inferences.  We plot the maximum-likelihood values for all the global paramters to show their variation across our `num_batches` independent runs of inference.  This corresponds to Table S1 in the supplemental materials."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "TZqHM3nIQ8Zj"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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162iVTKPI4T2pvXv3DrldkiS88847A9aHh4ejtrZ25JURkU9w9JjLE088gfT0dEiShLq6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\nIhIWQ4qIiIT1/wBaRBLoa7Z0JwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 600x400 with 6 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "fig, axs = plt.subplots(2, 3)\n",
        "axs[0, 0].boxplot(best_parameters.documented_infectious_tx_rate,\n",
        "                  whis=(2.5,97.5), sym='')\n",
        "axs[0, 0].set_title(r'$\\beta$')\n",
        "\n",
        "axs[0, 1].boxplot(best_parameters.undocumented_infectious_tx_relative_rate,\n",
        "                  whis=(2.5,97.5), sym='')\n",
        "axs[0, 1].set_title(r'$\\mu$')\n",
        "\n",
        "axs[0, 2].boxplot(best_parameters.intercity_underreporting_factor,\n",
        "                  whis=(2.5,97.5), sym='')\n",
        "axs[0, 2].set_title(r'$\\theta$')\n",
        "\n",
        "axs[1, 0].boxplot(best_parameters.average_latency_period,\n",
        "                  whis=(2.5,97.5), sym='')\n",
        "axs[1, 0].set_title(r'$Z$')\n",
        "\n",
        "axs[1, 1].boxplot(best_parameters.fraction_of_documented_infections,\n",
        "                  whis=(2.5,97.5), sym='')\n",
        "axs[1, 1].set_title(r'$\\alpha$')\n",
        "\n",
        "axs[1, 2].boxplot(best_parameters.average_infection_duration,\n",
        "                  whis=(2.5,97.5), sym='')\n",
        "axs[1, 2].set_title(r'$D$')\n",
        "plt.tight_layout()"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "Undocumented_Infection_and_the_Dissemination_of_SARS-CoV2.ipynb",
      "toc_visible": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}
